(i)
Let \(\mathsf {X}=[0,T]\) , let \(\mathsf {Y}=[-V/2,V/2]\)  and let \({H}\subset \mathsf {Y}^{\mathsf {X}}\)  be a class of functions with total variation at most \(V\) , for some \(T,V>0\) . Further, let \(_{H}\)  be the corresponding \(\mathrm {L}^1\) -metric (with respect to the Lebesgue measure). Then, in [1]} it has been shown that
\(\mathcal {N}(\epsilon ,{H},_{H})\le 2^{13VT/\epsilon }.\) 
(ii)
Let \(\mathsf {X}\subset \mathbb {R}^d\)  be compact and let \({H}\subset \mathcal {C}^\gamma (\mathsf {X},\mathbb {R})\)  be bounded (with respect to the corresponding Hölder metric) for some \(0<\gamma \le 1\) .
Then, for \(_{H}\)  being the Hölder or sup-metric, in [2]} it has been shown that there is \(C>0\)  such that
\(\mathcal {N}(\epsilon ,{H},_{H})\le \mathrm {e}^{C\epsilon ^{-2d/\gamma }}.\) 

